Question: Rewrite as a simplified fraction. ${0.9\overline{12} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 912.1212...\\ 10x &= 9.1212...\end{align*}}$ Subtracting the two equations, we have: ${990x = 903}$ ${x = \dfrac{903}{990}} $ ${x = \dfrac{301}{330}} $